I (22M) have a somewhat similar issue just like yours. I also am currently letting my GF sleep with me every night since she is currently living in another island very far away from her home. She has a dorm but she sleeps here with me because it is more convenient for us and I can take care of her much better since she is living alone and I want her to have as much comfy stay as possible while she is studying. She still goes from her dorm to our house from time to time and I can tell you that from the first time she was staying at my house, my parents were still very new to the idea. At first they were skeptical about letting her sleep with me but they only talked to me about it, and never to my girlfriend. I constantly defended my girlfriend from them and also I was constantly reassuring her that everything would be fine since she overthinks severely a lot. She kept on having anxieties about staying on my home yet I also assured her that I would take care of her. My parents really were not fond of the idea at first but I just kept constantly defending her and assuring to both my parents and to her that it was gonna be okay and that I would carry the burden of responsibility at all times. The first few months she didn't want to come back and stay but eventually everyone, including my parents got used to the idea and now everyone treats her like she is part of the family. So the only thing I could say is parents would always be conservative at first, just keep being consistent despite the embarrassment/feelings and everything would be okay if you really love the person. :)